Lily Has been traveling around the country. Last week, she spent $252 on fuel. If she spent $42 Each time She filled her Gas tank, How many times did she have to fill up? [Show The Equation With Algebra]

The correct answer is row number 16 since the sum is 65536 in

pascal's triangle which equals to the 2 power of 16 , that is 4th option.

Pascal's triangle, in algebra, a triangular arrangement of numbers that gives the coefficients in the expansion of any binomial expression, such as (x + y)n. This triangle is the triangular array of numbers that begins with 1 on the top and with 1's running down the two sides of a triangle. In any row of Pascal's triangle, the sum of the first, third, fifth, … numbers is equal to the sum of the second, fourth, sixth numbers.

(1+x)n=(n0)+(n1)x+(n2)x2+⋯+(nr)xr+⋯+(nn−1)xn−1+(nn)xn.

We know that , 2^16 = 65536

Therefore, the numbers come from the row number.16

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The number which is absent in the first 31 digits of pi = 0

We know that a number pi is nothing but the ratio of the circumference of a circle to its diameter.

It is represented by a symbol 'π'

pi is an irrational number. This means that it is not equal to the ratio of any two whole numbers.

Its digits do not repeat.

An approximation 3.14 or 22/7 is often used for everyday calculations.

To 31 decimal places, the value of pi is 3.1415926535897932384626433832795

The numbers present in the first 31 digits of pi are:

1, 2, 3, 4, 5, 6, 7, 8, 9

Only '0' is not present.

Therefore, the number which is absent in the first 31 digits of pi = 0

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Answer:

20

Step-by-step explanation:

Answer:

Step-by-step explanation:

-1.2x=12  divide both sides by -1.2 to get x alone

x= 10

x/9=4 multiply both sides by 9

x=36

Answer:

1. 10:35

2. 35: 45

3. 40: 50

Answer:

1. 10:35

2. 35: 45

3. 40: 50

Step-by-step explanation:

Answer:

23.41

Step-by-step explanation:

AB is gotten using the pythagoras theorem

AB² =  AC² + BC²

AB² = 22² + 8²

AB² = 484 + 64

AB² = 548

AB = √548

AB = 23.41

Hence the length of AB is 23.41

29-3f+2g

=29-3(4)+2(3)

=29-12+6

=23

It's false. Take x = -1, then

cos⁻¹(-(-1)) = cos⁻¹(1) = 0

but

-cos⁻¹(-1) = -π

Step-by-step explanation:

- x + 17 = 45

- x = 45 - 17

- x = 28

x = - 28

Hope it helped.

Answer:

x = -28

Step-by-step explanation:

Subtract the 17 from both sides to get -x = 28

Divide both sides by negative one to isolate the x and get x = -28

A secant line is a line which intersects a circle at exactly 2 points.  

Line DA is a secant because it matches this criteria.

Hope this helps :)

Answer:

1)a) $4.20

1)b) $1.05

1)c) 28.6%

2)a) $0.73

2)b) $35.20

Step-by-step explanation:

1)a)

Beans after discount $3.00

Discount $1.20

Before discount $3.00 + $1.20 = $4.20

1)b)

Original price $4.20

4 cans

Price per can $4.20/4 = $1.05

1)c)

Percent discount $1.20/$3.00 × 100% = 28.6%

2)a)

1 box $4.40, 6 fillets

$4.40/6 = $0.73

Price for 1 fillet: $0.73

2)b)

1 box $4,40

8 boxes 8 × $4.40 = $35.20

The second option shows a pair of triangles which are congruent by the SSS congruence theorem.

The SSS (Side - Side - Side) congruence theorem states that if two triangles have three sides that are congruent to each other, then the two triangles are congruent by the SSS theorem.

The congruent sides for the second option are given as follows:

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Answer:12x+64

Step-by-step explanation:

you x 8 and 3 (expand the bracket) and then x 8 and 8 =64

The fifth degree polynomial is P(x) = x⁵ - 5x⁴ + 5x³ + 20x² 36x + 20

From the question, we have the following parameters that can be used in our computation:

Degree = 5

Roots = (2-i), 2, -2 and 1

There is a complex root in the roots

So, the last root is 2 + i

The polynomial is then calculated as

P(x) = (x - roots)^multiplicity

So, we have

P(x) = (x - 2)(x + 2)(x - 1)(x - 2 + i)(x - 2 - i)

Evaluate

P(x) = (x² - 4)(x - 1)((x - 2)² + 1)

Expand

P(x) = (x² - 4)(x - 1)(x² - 4x + 5)

This gives

P(x) = (x³ - x² - 4x + 4)(x² - 4x + 5)

Lastly, we have

P(x) = (x⁵ - 4x⁴ + 5x³ - x⁴ + 4x³ - 5x² - 4x³ + 16x² - 20x + 4x² - 16x + 20)

Evaluate the like terms

P(x) = x⁵ - 5x⁴ + 5x³ + 20x² 36x + 20

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Given that the discharge current decreases to 27% of its initial value in 1.40 ms, we can use the equation of discharge current:

The capacitance of the capacitor is 0 F.

Part A:

Given that the discharge current decreases to 27% of its initial value in 1.40 ms, we can use the equation of discharge current:

I = I₀e^(-t/RC)

Here,

I₀ = initial current

R = resistance

C = capacitance

t = time

We are given that the current is 27% of the initial value, so the equation becomes:

0.27 = \(1e^(-1.40*10^-3/RC)\)

Simplifying the equation, we find:

RC =\(3.28* 10^-3 s\)   ----(1)

Part B:

The time taken to discharge a capacitor through a resistance R is given by:

t = RC ln (Vc/V₀)

where Vc = voltage across the capacitor at time t and V₀ = initial voltage across the capacitor.

Substituting the values, we have:

\(1.40*10^-3\) = C*90 ln (0/100)

Since a fully discharged capacitor has a voltage of 0, we set Vc = 0. Thus, the equation becomes:

\(1.40*10^-3\)= C*90 ln (0)

The natural logarithm of 0 is negative infinity. Therefore, the equation becomes:

\(1.40*10^-3\)= C*90*(-infinity)

Simplifying further, we find:

C = 0

Thus, the value of capacitance is 0 F.

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Answer:

Step-by-step explanation:

Answer:

59049

Step-by-step explanation:

La razón es multiplicar por 3

Entonces:

ya que inicia en tres y se multiplica por tres, el décimo término es:

3¹⁰ = 59049

Comprobación:

       3

3*3=9

9*3 =27

27*3 = 81

81*3 = 243

243*3 = 729

729*3 = 2187

2187*3 = 6561

6561*3 = 19683

19683*3 = 59049

A scale factor is defined as the ratio between the scale of a given original object and a new object,

The side length of the photo is 3 inches.

A scale factor is defined as the ratio between the scale of a given original object and a new object.

We have,

Emma wants to enlarge a square photo and print it on a square canvas.

The side length of the canvas is 12 inches.

The scale from the canvas to the photo is 4 inches.

This means,

Scale factor = Canvas side / Photo side

4 = 12 inches/side length of the photo

Side = 12/4

Side = 3 inches

Thus,

The side length of the photo is 3 inches.

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Answer:

send u questioonn

Step-by-step explanation:

properly

Answer:

To find the area of a quarter circle, find the area of the whole circle by using the formula A = pi * r^2 and then divide by 4. To find the perimeter of the quarter circle, find the circumference of the whole circle, divide by 4, and then add the radius twice.

The distances from the new wine to Cluster 1, Cluster 2, and Cluster 3 are not provided, so it is not possible to give a specific answer.

The distances would depend on the specific data and the distance metric used to calculate them.

In order to answer the question accurately, the distances between the new wine and each cluster would need to be calculated using a suitable distance metric, such as Euclidean distance or Manhattan distance. Without this information, it is not possible to provide a precise answer.

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Answer:

x = 2

Step-by-step explanation:

Simplifying

4(2x + -1) = 12

Reorder the terms:

4(-1 + 2x) = 12

(-1 * 4 + 2x * 4) = 12

(-4 + 8x) = 12

Solving

-4 + 8x = 12

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.

-4 + 4 + 8x = 12 + 4

Combine like terms: -4 + 4 = 0

0 + 8x = 12 + 4

8x = 12 + 4

Combine like terms: 12 + 4 = 16

8x = 16

Divide each side by '8'.

x = 2

Simplifying

x = 2

hope it helps

The linear equations representing the scenario are:

A system of linear equations involves two linear equations with two variables.

One equation represents the total cost function, including fixed and variable costs.

The second equation represents the total revenue function.

The variable cost for growing and harvesting coffee per kilogram = $0.70

The fixed costs for land management per year = $2,000

Let x = the quantity of coffee in kilograms

Total cost, t = 2,000 + 0.7x

Revenue per kilogram = $1.20

Total revenue, y = 1.20x

Thus, the farmer's total revenue and cost functions can be represented by the following two linear equations: a) y = 1.20x  and b) t = 2,000 + 0.7x.

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980g of sulphuric acid (H₂SO₄) is needed to prepare 5.0L of a 2M solution.

So, the grams of H₂SO₄ needed will be:

Therefore, 980g of sulphuric acid (H₂SO₄) is needed to prepare 5.0L of a 2M solution.

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Answer:

The one to the right

Step-by-step explanation:

(c) To find the unique Bayesian Nash Equilibrium (BNE), we need to consider player 1's beliefs about nature's move and player 2's strategies.

In this game, player 1 observes nature's move, so player 1's information set is {A, B}. Player 1's strategy is to choose either L or R given their beliefs about nature's move. Let's denote player 1's strategy as s1(L) and s1(R). Player 2's strategies are U and D. Let's denote player 2's strategy as s2(U) and s2(D).

To find the BNE, we need to find the combination of strategies that maximize the expected payoffs for both players. In this case, the BNE can be determined as follows: If nature chooses A, player 1 should choose s1(L) to maximize their payoff (0). If nature chooses B, player 1 should choose s1(R) to maximize their payoff (-3). For player 2, they should choose s2(U) to maximize their payoff (-20) regardless of nature's move. Therefore, the unique BNE is (s1(L), s2(U)). The expected equilibrium payoffs for both players are:  Player 1: E1 = 0.5(0) + 0.5(-3) = -1.5. Player 2: E2 = 0.5(-20) + 0.5(-20) = -20

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Answer:

its 444

Step-by-step explanation:

Answer:

X= sin (56) . 17) hope this helps

The properties of the graph are

The equation of the function is given as

f(x) = (x - 2)(x + 6)

The above equation is a quadratic function.

Next, we plot the equation on a graph (see attachment)

Set x = 0 to determine the y-intercept

y-intercept = (0 - 2)(x + 6)

y-intercept = -12

Expand the function to determine the symmetry axis

f(x) = x^2 - 2x + 6x - 12

Differentiate and set to 0

2x - 2 + 6 = 0

This gives

x = -2 --- axis of symmetry

Substitute x = -2 in the function to calculate the vertex/Min/Max

f(-2) = (-2 - 2)(-2 + 6)

f(-2) = -16

This means that

Direction = Up, Min = -16 and Vertex = (2, -16)

Set the function to 0 to determine the roots

(x - 2)(x + 6) = 0

Solve for x

x = 2 and x = -6

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